Towards Programmable Microfluidics

William Thies*, Mats Cooper†, David Wentzlaff*, Todd Thorsen†, and Saman Amarasinghe*

* Computer Science and Artificial Intelligence Laboratory† Hatsopoulos Microfluids Laboratory

Massachusetts Institute of Technology

April 15, 2004

Microfluidic Chips• Idea: a whole biological lab on a single chip

– Input channels for reagants– Chambers for mixing fluids– Actuators for modifying fluids

•Temperature - Ultraviolet radiation•Light/dark - Electrophoresis

– Sensors for reading properties•Luminescence - Immunosensors•pH - Glucose

• Starting to be manufactured and used today

• Active area of research

Microfluidic Applications

• Biochemistry– Enzymatic assays– The Polymerase Chain Reaction– Nucleic acid arrays– Biomolecular separations– Immunohybridization reactions– Piercing structures for DNA injection

Microfluidic Applications

• Biochemistry

• Cell biology– Flow cytometry / sorting– Sperm/embryo tools: sperm motility, in vitro

fertilization, embryo branding– Force measurements with bending cantilevers– Dialectrophoresis / electrorotation– Impedance monitoring for cell motility and

micromotion– Chemical / physical substrate patterning

Microfluidic Applications

• Biochemistry

• Cell biology

• General-Purpose Computing– Compute with fluids– Not our current interest

Microfluidic Applications

• Biochemistry

• Cell biology

• General-Purpose Computing

• Summary of Benefits:– High throughput– Small sample volumes– Geometric manipulation– Portable devices– Automatic Control

• Current interface: gate-level control (e.g., Labview)

• New abstraction layers will enable:– Scalability

• Currently have 1,000 storage cells, can manage resources by hand

• Soon will have 1,000,000: how to manage complexity? – Portability

• Hide architecture-specific details from programmer• Same experiment works on successive generations of chips

– Modularity• Create reusable components• Enable large and complex procedures

– Adaptivity• Use real-time sensor feedback to guide experiment • Adjust procedure to suite field conditions

Our Goal:Provide Abstraction Layers for

this Domain

• Current interface: gate-level control (e.g., Labview)

• New abstraction layers will enable:– Scalability

• Currently have 1,000 storage cells, can manage resources by hand

• Soon will have 1,000,000: how to manage complexity? – Portability

• Hide architecture-specific details from programmer• Same experiment works on successive generations of chips

– Modularity• Create reusable components• Enable large and complex procedures

– Adaptivity• Use real-time sensor feedback to guide experiment • Adjust procedure to suite field conditions

Our Goal:Provide Abstraction Layers for

this Domain

Our Contributions

1. End-to-end programmable system– General-purpose microfluidic chip– High-level software control

2. Novel mixing algorithms– Mix k fluids in any concentration (± 1/n)– Guarantees minimal number of mixes:

O(k log n)

Outline

• Introduction• Mixing algorithms• General-purpose microfluidic chip• Portable programming system• Implementation• Related Work• Conclusions

Outline

• Introduction• Mixing algorithms• General-purpose microfluidic chip• Portable programming system• Implementation• Related Work• Conclusions

Mixing in Microfluidics

• Mixing is fundamental operation of microfluidics– Prepare samples for analysis– Dilute concentrated substances– Control reagant volumes

• Important to mix on-chip– Otherwise reagants leave system whenever mix

needed– Enables large, self-directing experimentsAnalogous to ALU operations on microprocessors

The Mixing Problem

• Experiments demand mixing in arbitrary proportions– For example, mix 15% reagant / 85% buffer

– Users should operate at this level of abstraction

• However, microfluidic hardware lacks arbitrary mixers– Most common model: 1-to-1 mixer

• Important optimization questions:– What mixtures are reachable?– How to minimize reagant consumption?– How to minimize number of mixes?

1 unit of Amix

1 unit of B

50% A 50% B1 unit of

Why Not Binary Search?0 13/8

1/41/2

1/23/8 5 inputs, 4 mixes

Why Not Binary Search?0 13/8

3/41/2

3/8

4 inputs, 3 mixes

1/41/2

1/23/8 5 inputs, 4 mixes

Mixing Trees

• Properties:– Mixing trees are binary trees– Leaf nodes: unit sample of an input fluid– Internal nodes: result of 1-to-1 mix of children– Evaluate from bottom to top

• Observation:– # leaf nodes = # internal nodes + 1 (induction on #

nodes)

– Minimizing mixes and reagant usage is equivalent

{(A, ½), (B, ½)}

{A} {B}

# reagants used = # mixes + 1

{A}

{B} {C}

{C}

{(B, ½), (C, ½)}

{(A, ½), (B, ¼), (C, ¼)}

{(A, ¼), (B, 1/8), (C, 5/8)}

Mixing Trees

Theorem: For substance S, let nd denote number of leaf nodes at depth d. Then overall concentration for S is d nd * 2-d

Proof: Substance is diluted 2X at each step, and final mixture is sum over all child nodes.

{A}

{B} {C}

{C}

{(B, ½), (C, ½)}

{(A, ½), (B, ¼), (C, ¼)}

{(A, ¼), (B, 1/8), (C, 5/8)}depth = 0

depth = 1

depth = 2

depth = 3

Example: {C}

conc = 2-1 + 2-3

conc = 1/2 + 1/8

conc = 5/8

Reachable Mixtures• Theorem: A mixture is reachable if

and only if it can be written:

{(S1, p1/2d), (S2, p2/2d), … , (Sk, pk/2d)}

• Proof:

Must be mixing tree for mixture

Expand to balanced tree

Each leaf node contributes 1/2d

p1 p2 p3

S1 S1S1 S2 S2S2 S2 S3

i pi = 2d

A=3 B=5 =0011 =0101

B

A

A B

Min-Mix Example 2• Recall example: mixture {(A, 3/8), (B,

5/8)}bins

23 = 8

22 = 4

21 = 2

20 = 1

c = 2-2 + 2-3 = 1/4 + 1/8

= 3/8

depth = 1

depth = 0

depth = 2

depth = 3

c = 2-1+2-3 = 1/2 + 1/8

= 5/8

3 mixesSame as optimal

A=5 B=7 C=4 =00101 =00111 =00100

A B C

B

A B

Min-Mix Example 2• Mixture {(A, 5/16), (B, 7/16), (C, 4/16)}

bins

24 = 16

23 = 8

22 = 4

21 = 2

20 = 1

B CA

B

A B

• Correctness intuition: put d’th most significant bit at depth d• Can always build tree: induction on # bits at depth d

Min-Mix Algorithmnode buildMixingTree(mixture {(S1, p1/n), ..., (Sk, pk/n)}) { depth = lg(n) bins = new stack[depth+1] for i = 1 to k for j = 0 to depth-1 if (j’th least significant bit of pi =1) { bins[j].push(Si) } return buildMixingHelper(bins, depth)}

node buildMixingHelper(stack[] bins, int pow) { if bins[pow].empty() then node child1 = buildMixingHelper(bins, pow-1) node child2 = buildMixingHelper(bins, pow-1) return <child1, child2> as internal node; else return bins[pow].pop() as leaf node; endif}

bins[4] = { }bins[3] = { }bins[2] = { A, B, C}bins[1] = { B }bins[0] = { A, B }

pow43210

A

A

B

B

B

C

A

A

B

B

B

C

Optimality of Min-Mix

• Consider mixture: {(S1, p1/n), … , (Sk, pk/n)}

• Number of input samples used = number of bits in representation of inputs

• Theorem: this is optimal reagant usage– Implies optimal number of mixes

• Proof: otherwise some pi/n is unattainable

• Asymptotic reagant usage: O(k lg n)– This is also runtime of Min-Mix (visits nodes once)

A

A

B

B

B

C

Supporting Error Tolerances

• What if user wants to mix {(A, 1/3), (B, 2/3)}?– Impossible to obtain exactly with 1-to-1

mixer– However, can approximate within

tolerance, ± – Error bounds are natural part of all

experiments

Supporting Error Tolerances• Method: increase mixing depth d until some mix

p1/2d … pk/2d falls within desired ranges

– Example: mix {(A, 1/3), (B, 1/3), (C, 1/3)} ± 0.05?•Each substance should fall in range [0.23, 0.43]

Depth Concentrations

1 0.5 - Out of range 2 0.25,0.5,0.75 - In range, but infeasible:

0.25 + 0.25 + 0.25 < 1 3 …, 0.25, 0.375, … - In range and feasible:

0.25 + 0.375 + 0.375 = 1

- Could be multiple solutions; we choose greedily

0 1

Outline

• Introduction• Mixing algorithms• General-purpose microfluidic chip• Portable programming system• Implementation• Related Work• Conclusions

What Does General-Purpose Mean?

• Computing: Turing Machine– Implementation parameter: memory size

• Microfluidics: “Universal Fluidic Machine”

– Implementation parameters:•memory size precision sensors/agitators

Tape of Buckets

… …Oracle Sensors

Classical TuringMachine

(For Control)

Oracle Agitators

…Tape of Buckets

… …Oracle Sensors

Classical TuringMachine

(For Control)

Oracle Agitators

…

Our General-Purpose Chip (April 2004)

Control layerFlow layer

5 mm

Our General-Purpose Chip (April 2004)

Control layerFlow layer

Control ports

Mixer

Purge Out

Wash In

5 mm

• 8 storage cells

• Individually addressable

• 9 picoliters each

Storage Cells

Multiplexor

• Rotary mixer (Quake et al.)

• Input / Output

• Can also add I/O ports to storage cells

Chip-Level Operations• All operations are

“pushed” by input, flow to purge out

• Extra inputs / outputs attached to storage cells

• Basic operations:– storage output– storage mixer– mixer storage

• Due to precision limits, output of mixer only fillsone storage cell

• storage storage is“mix 2 of same fluid and store”

Wash In

Purge Out

A

B

Outline

• Introduction• Mixing algorithms• General-purpose microfluidic chip• Portable programming system• Implementation• Related Work• Conclusions

A Portable Machine Language (PML)

• C is PML for von-Neumann machines- Hides idiosyncratic differences- Exposes important properties - Enables portability

• Things to virtualize in microfluidic realm:– # of chambers, pipes, mixing reservoirs, etc.– Location of fluids on the chip– Precision of mixing and routing hardware– Timing of events

• Our solution: Lava– A Java library with first-class Fluid objects– Virtualizes basic resources– Provides native hooks for common agitators /

sensors

Lava System Architecture

Example: Recursive Descent Search

• Goal: find ratio of two fluids with highest activity– Common question in biology

• Modeling activators / inhibitors• Understanding signaling pathways• Drug discovery

• Method: zoom in on area of interest

set range = [0,1]for each round {

for each point p in range {measure activity at p

}adjust range around highest activity

}report range and activity

Round:

Range:

1 2 3

Example: Recursive Descent Search

interface SimpleEngine extends FluidEngine { Fluid input(Integer i); // require array of fluid inputs Double luminescence(Fluid f); // require luminescence camera}

class RecursiveDescent { public static void main(String[] args) { SimpleEngine engine = (SimpleEngine) // build engine for interface EngineFactory.buildEngine("SimpleEngine", MY_BACKEND); run(engine); }

static void run(SimpleEngine engine) { … }}

Example: Recursive Descent Search static void run(SimpleEngine engine) {

Fluid A = engine.input(new Integer(0)); // input Fluids Fluid B = engine.input(new Integer(1)); double center = 0.5, radius = 0.5; // set range of interest double act, bestActivity = -1;

for (int i=0; i<ROUNDS; i++) { // repeat a number of rounds int bestJ = 0; for (int j=0; j<10; j++) { // try 10 samples double target = center+radius*(1-2*(double)j/10); Fluid f = engine.mix(A, target, B, 1-target); // prepare mixture engine.waitFor(30); act = engine.luminescence(f).doubleValue(); // measure activity if (act > bestActivity) { bestActivity = act; bestJ = j; // remember highest activity }} center = center+radius*(1-2*(double)bestJ/10); // zoom in on highest activity radius = radius / 2; } System.out.println("Highest activity at: " + center); }

Providing Digital Abstraction

• Challenge: Fluid variables used multiple times– But once a fluid is used on-chip, it is gone!– This is a lossy system– Need to provide some notion of GAIN

Providing Digital Abstraction

• Challenge: Fluid variables used multiple times

• Solution: re-generate fluids on demand– Lava traces history for computing each Fluid

– Current model: stateless mixing, native functions– If unavailable fluid referenced, re-evaluate history

• Optimizations– Lazy evaluation– Evaluate in order that minimizes temporaries

input (0)

input (1)mix wait(30)

input (0)mix heat(10)

Outline

• Introduction• Mixing algorithms• General-purpose microfluidic chip• Portable programming system• Implementation• Related Work• Conclusions

Implementation Status (April 2004)

• Prototype chip fabricated

• Demonstrated I/O, moving fluids, mixing

• Current focus:– Robustness

• Air bubbles• Diffusion

– Calibration• Need to

determinetiming for automatic control

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

0. Start with mask of channels

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

1. Deposit pattern on silicon wafer

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

2. Pour PDMS over mold - polydimexylsiloxane: “soft lithography”

Thick layer (poured)

Thin layer (spin-coated)

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

3. Bake at 80° C (primary cure), then release PDMS from mold

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

4a. Punch hole in control channel4b. Attach flow layer to glass slide

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

5. Align flow layer over control layer

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

6. Bake at 80° C (secondary cure)

Fabrication Process (Quake et al.)

Control Layer

Flow Layer

pressure

actuator

7. When pressure is high, controlchannel pinches flow channel toform a valve

Making a Multiplexor (Thorsen et al.)

flow layercontrol layer

Bit 2 Bit 1 Bit 00 1 0 1 0 1

Input

Output 0

Output 7

Output 6

Output 5

Output 4

Output 3

Output 2

Output 1

• Control lines can cross flow lines - Only thick parts make valves

• Logic is not complimentary

• To control n flow lines, need 2 log2 n control lines

Making a Multiplexor (Thorsen et al.)

Bit 2 Bit 1 Bit 00 1 0 1 0 1

Input

Output 0

Output 7

Output 6

Output 5

Output 4

Output 3

Output 2

Output 1

• Control lines can cross flow lines - Only thick parts make valves

Example: select 3 = 011

flow layercontrol layer

• Logic is not complimentary

• To control n flow lines, need 2 log2 n control lines

Making a Multiplexor (Thorsen et al.)

Bit 2 Bit 1 Bit 00 1 0 1 0 1

Input

Output 0

Output 7

Output 6

Output 5

Output 4

Output 3

Output 2

Output 1

• Control lines can cross flow lines - Only thick parts make valves

Example: select 3 = 011

flow layercontrol layer

• Logic is not complimentary

• To control n flow lines, need 2 log2 n control lines

Making a Multiplexor (Thorsen et al.)

• Logic is not complimentary

• To control n flow lines, need 2 log2 n control lines

Bit 2 Bit 1 Bit 00 1 0 1 0 1

Input

Output 0

Output 7

Output 6

Output 5

Output 4

Output 3

Output 2

Output 1

• Control lines can cross flow lines - Only thick parts make valves

Example: select 3 = 011

flow layercontrol layer

Our Multiplexor in Operation

Water

Dye

Open Valve

Closed Valve

Scaling to Large Chips (Thorsen et al.)

• 1000 individually addressable chambers

• Uses row multiplexor, column multiplexor

• With industrial fabrication processes, will be possible to scale much further

Rotary Mixer (Quake et al.)

Mode of operation: 1. Fill left with reagant

A 2. Fill right with

reagant B 3. Lock down I/O 4. Use mixer valves as

peristaltic pump Channel mixes due to difference in inner / outer rotational velocities

Our Mixer in Operation

Outline

• Introduction• General-purpose microfluidic chip• Portable programming system• Mixing algorithms• Related work• Conclusions

Related Work• Droplet-based microfluidics (Fair et al.)

– Manipulate discrete droplets using electrowetting– Pro:

• Flexible grid of cells• No diffusion• Conventional fabrication

process– Con:

• Unclear if droplets can scale down (currently 100X larger than our storage chambers)

• Non-polar reagants cannot be manipulated• Imprecise dispensing and splitting of droplets

– Droplets vs. continuous flow will be ongoing debate

• Lava can target a droplet-based machine– Easy to emulate mixer, storage on chip

Related Work

• Mixing for droplets (Fair et al.)– Seems to suggest binary-search procedure

•O(n) mixes to obtain concentration p/n•Only deals with two fluids•Slightly different model of computation

– Our algorithm is improvement: O(k lg n)

• Quake et al. – continuous flow microfluidics– Two-layer soft lithography, rotary mixer,

PCR– Our work relies on these foundations

Outline

• Introduction• General-purpose microfluidic chip• Portable programming system• Mixing algorithms• Related work• Conclusions

Future Work

• Mixing Algorithms– Generalize 1-to-1 mixing model to N-to-M mixer– Find mixing tree with minimal storage– Exploit error tolerances to optimize mixing

• Software– Expand language to encompass broader idioms

• Can we simulate an entire cell on-chip?– Scheduling optimizations: re-order computation– Verification of safety properties

• Hardware– Integrate sensors / agitators on chip– Develop CAD tools for micofluidic domain– Explore parallel hardware constructs

Conclusions• Microfluidic is the next big thing in biology• Many opportunities for computer scientists• Our contributions:

1. End-to-end programmable system- Universal Fluidic Machine- General-purpose microfluidic chip- Lava: portable, high-level language

2. Novel mixing algorithm- Mix k fluids with precision ± 1/n: O(k lg n) mixes- Guarantees optimal reagant usage, # of mixes

• Vision: create de-facto language for experimental scientists

– Replicate a published experiment on your own microfluidic chip